JEE Advance - Mathematics (1978 - No. 9)
A straight line segment of length $$\ell $$ moves with its ends on two mutually perpendicular lines. Find the locus of the point which divides the line segment in the ratio $$1 : 2$$
$$9{x^2} + 36{y^2} = {4\ell}$$
$$9{x^2} - 36{y^2} = 4{\ell ^2}$$
$$9{x^2} + 36{y^2} = 4{\ell ^2}$$
$$36{x^2} + 9{y^2} = 4{\ell ^2}$$
$$36{x^2} + 9{y^2} = {4\ell}$$